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Liao, S.J. (1992) On the Proposed Homotopy Analysis Techniques for Nonlinear Problems and Its Application. Ph.D. Dissertation, Shanghai Jiao University, Shanghai.

has been cited by the following article:

• TITLE: A Mathematical Approach Based on the Homotopy Analysis Method: Application to Solve the Nonlinear Harry-Dym (HD) Equation

  AUTHORS: Emran Khoshrouye Ghiasi, Reza Saleh

  KEYWORDS: Harry-Dym (HD) Equation, Soliton, Homotopy Analysis Method (HAM), Auxiliary Parameter, Convergence Analysis, Relative Error

  JOURNAL NAME: Applied Mathematics, Vol.8 No.11, November 13, 2017

  ABSTRACT: In this paper, the homotopy analysis method (HAM) has been employed to obtain the approximate analytical solution of the nonlinear Harry-Dym (HD) equation, which is one of the most important soliton equations. Utilizing the HAM, thereby employing the initial approximation, variations of the 7th-order approximation of the Harry-Dym equation is obtained. It is found that effect of the nonzero auxiliary parameter on convergence rate of the series solution is undeniable. It is also shown that, to some extent, order of the fractional derivative plays a fundamental role in the prediction of convergence. The final results reported by the HAM have been compared with the exact solution as well as those obtained through the other methods.